Hello and welcome to TSF
I doubt your problem is bios releated; however with computers anything is possible
most likely your trouble is either / cpu overheating or memory errors of voltage problem
but if you want to update with the bios we can ? you would be better off waiting until you get the system stable before you try updating your bios / if your computer shutsdown during a bios update you will be left with a system that wont do anything
until you buy a new bios chip
before we head down that road / lets some some "other" stuff first
A) download memtest / its dos bootable and will check your memory for errors without needing to boot into windows
here is the floppy disk version:
http://www.majorgeeks.com/Memtest86_d1247.html
here is the cd-rom version:
http://www.majorgeeks.com/Memtest86_d4226.html
B) check in your system bios and verify what the temperature of the CPU is and also report your system voltages
C) you can also test your hard drive with this bootable CD >>>> open your computer and verify who is the manufacturer of your boot drive >>> then run the diagnostic according to the drive manufacturer ??
http://www.ultimatebootcd.com/
from within the Ultimate boot CD you can run "CPU Burn In" that will show your cpu temps >>>> check your temps when you first run the program
give us a shout if you need help with any of these / and give us the results of your diangostic troubleshooting
best regards
joe